Marin Elevation

marin %$%
  plot_ly(x = x, y = y, z = z) %>%  
  add_surface() 

d %>% 
  ggplot(aes(x=x,y=y)) + 
  stat_density_2d(aes(fill = ..level..), geom = 'polygon') +
  geom_segment(aes(x = 8.75, y = 10, xend = 9.5, yend = 10), size = 1.5) + 
  geom_text(aes(x = 10, y = 10), label = 'North', angle = 270, size = 5) +
  scale_y_continuous(limits = c(0, 90)) + 
  labs(title = 'Functional Headlands') + 
  theme_minimal() + 
  theme(legend.position = 'none')

# ggsave(
#   filename = './images/marin_density.pdf',
#   device = 'pdf', bg = 'transparent')

d %>% 
  ggplot(aes(x=x,y=y)) + 
  geom_density_2d() +
  scale_y_continuous(limits = c(0, 90)) + 
  geom_segment(aes(x = 8.75, y = 10, xend = 9.5, yend = 10), size = 1.5) + 
  geom_text(aes(x = 10, y = 10), label = 'North', angle = 270, size = 5) +
  labs(
    title = 'Functional Headlands'
  ) + 
  theme_minimal()

# ggsave(
#   filename = './images/marin_contour.pdf', 
#   device = 'pdf', bg = 'transparent')

d %>% 
  ggplot(aes(x=x,y=y)) + 
  geom_density_2d() +
  geom_segment(
    aes(x = 0, xend = 10, y = (-200/30), yend = (-200/30) + 80),
    size = 2, color = 'darkorange') +
  stat_function(
    fun = function(x) 10 - 2*x + x^2, xlim = c(0,10), 
    size = 2, color = 'steelblue') +  
  geom_segment(aes(x = 8.75, y = 10, xend = 9.5, yend = 10), size = 1.5) + 
  geom_text(aes(x = 10, y = 10), label = 'North', angle = 270, size = 5) +
  labs(
    title = 'Functional Headlands'
  ) + 
  theme_minimal()

# ggsave(
#   filename = './images/marin_contour_highest_prob.pdf', 
#   device = 'pdf', bg = 'transparent')

y <- seq(9, 90, by = 0.1)
Fy <- .1 * sqrt(y-9) + .1
ecdf_y <- ecdf(sample(d$y, size = 20, replace = TRUE))

plot(
  ecdf_y, 
  main = 'CDF and Empirical CDF',
  col = 'steelblue')
lines(x=y, y=Fy, col = 'darkorange')

Student Example

x <- seq(0,2,.01)
fx <- .5*x

More complexity

d <- data.frame(
  id = 1:10000,
  x = c(
    runif(n=5000, min = 0, max = 10),
    runif(n=5000, min = 5, max = 15)
    ), 
  w = rnorm(n = 10000, mean = 0, sd = 3)
  )

d <- d %>%  
  mutate(
    y = ifelse(
      id <= 5000, 
      10 - 2*x + x**2 + w,
      -10 + 20*x - (x - 5)**2 + w
      ))

complex_marin <- d %$% 
  kde2d(x = x, y = y, n = 500)
complex_marin %$%
  plot_ly(x = x, y = y, z = z) %>%  
  add_surface() 

d %>% 
  filter(id %in% sample(1:n(), size = 100)) %$%
  kde2d(x=x,y=y, n=100) %$%
  plot_ly(x=x,y=y,z=z) %>%  
  add_surface()

complex_marin %>% 
  plot_ly(x=x, y=y, z=z) %>%  
  add_markers()

Error: First argument, `data`, must be a data frame or shared data.

l <- data.frame(
  lowess(d$x, d$y, f = .05)
)

d %>% 
  ggplot() + 
  geom_density_2d(aes(x=x,y=y)) + 
  geom_point(data = l, aes(x=x, y=y))

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